Automatic Synthesis of FSMs for Enforcing Non-functional Requirements on MPSoCs Using Multi-objective Evolutionary Algorithms

Embedded system applications often require guarantees regarding non-functional properties when executed on a given MPSoC platform. Examples of such requirements include real-time, energy, or safety properties on corresponding programs. One option to implement the enforcement of such requirements is by a reactive control loop, where an enforcer decides based on a system response (feedback) how to control the system, e.g., by adapting the number of cores allocated to a program or by scaling the voltage/frequency mode of involved processors. Typically, a violation of a requirement must either never happen in case of strict enforcement, or only happen temporally (in case of so-called loose enforcement). However, it is a challenge to design enforcers for which it is possible to give formal guarantees with respect to requirements, especially in the presence of typically largely varying environmental input (workload) per execution. Technically, an enforcement strategy can be formally modeled by a finite state machine (FSM) and the uncertain environment determining the workload by a discrete-time Markov chain. It has been shown in previous work that this formalization allows the formal verification of temporal properties (verification goals) regarding the fulfillment of requirements for a given enforcement strategy. In this article, we consider the so-far-unsolved problem of design space exploration and automatic synthesis of enforcement automata that maximize a number of deterministic and probabilistic verification goals formulated on a given set of non-functional requirements. For the design space exploration (DSE), an approach based on multi-objective evolutionary algorithms is proposed in which enforcement automata are encoded as genes of states and state transition conditions. For each individual, the verification goals are evaluated using probabilistic model checking. At the end, the DSE returns a set of efficient FSMs in terms of probabilities of meeting given requirements. As experimental results, we present three use cases while considering requirements on latency and energy consumption.